When we look at the sine wave motion in its typically down-up-down form we can identify it as a vertical* sine wave. With vertical I mean that the wave oscillates up and down. This motion is usually used in order to drop body weight onto the technique and works excellent for techniques with a slight or strong downward angle like a middle section punch or a side-fist downward strike. This sine wave motion can also be used in an upward direction; for example, when one does a forearm rising block you move from a relaxed position to an upward position. The final drop of the typical down-up-down motion is omitted as it will act contrary to the direction of the upward technique. The (vertical) sine wave motion is therefore employed for techniques where the force of the technique moves either up or down.
The sine wave can also occur horizontally*; in other words, the wave oscillates from left to right or vice-versa. Usually when we talk about this type of sine wave, we refer to hip rotation or hip twist. Typically the hip is pulled back slightly and then jerked in the direction that the blocking or attacking tool needs to travel. Hip rotation is often part of a whip-like action where the different parts of the body are accelerated and uncoiled to create kinetic chaining. Techniques that benefit from a horizontal wave typically move horizontally, for instance a back fist strike or a knife-hand side strike.
Do we combine (vertical) sine wave motion with hip rotation? Yes and no. It depends on the technique. A technique like a wedging block that uses two forearms moving horizontally in opposite directions do not use hip rotation because it is impossible to rotate your hips both left and right to accommodate both arms. For a wedging block we only use vertical sine wave motion. The forearm rising block is also a good example where the main force of the technique goes up; for this technique a horizontal wave, in other words hip rotation, is downplayed.
There are techniques where the main angle of the technique goes forward and downward and can therefore benefit from both the forward hip rotation as well as body dropping through the sine wave motion. A clear example would be a diagonal downward elbow strike (as seen the pattern Juche) or even just a forward stepping middle front punch. The middle front punch reaches its target in a slight downward angle. A further example is the low forearm block, which moves both downward and to the side.
Actually, the simple rotation of the fist during punching is in fact the combination of a vertical and horizontal sine wave. The rotation plus forward motion creates a spiral or helix, which can be described mathematically as the combination of a vertical and horizontal sine wave. These types of combined vertical and horizontal wave forms can often be seen in ITF Taekwon-Do by the trained eye.
The important thing is to understand the direction of the forces created by these waves and also the force directions required by the various techniques you are using. Certain techniques benefit more from a vertical sine wave, in other words the typical sine wave motion, while other techniques benefit more from a horizontal sine wave, in other words from hip rotation. Using or putting emphasis on the wrong wave form should be avoided as it may nullify the power of your technique. Also, different parts of the wave benefits different techniques. One should not drop your body weight at the end of a rising block, nor should you raise your body at the end of a low block. Similarly the hip should rotate towards the target, not away from it.
Learning how to use the different wave forms is crucial in mastering ITF Taekwon-Do.
* Please note that my reference to "vertical" and "horizontal" should not be confused with the use of these terms in the ITF Encyclopaedia's discussion on ways of stepping. I'm using the terms here to describe whether we are viewing a sine wave as depicted on a Y-axis (thus vertically) or Z-axis (thus horizontally).